A cylindrical syringe has a height of 6.8 cm and a diameter of 2.37 cm is going to be

Mathematics

1 answer:

alukav5142 [94]2 years ago

7 0

Answer:

The number of syringe filled with water that would be needed to fill the semi-sphere is approximately 8.714 syringes

Step-by-step explanation:

The height of the syringe = 6.8 cm

The diameter of the syringe = 2.37 cm

The circumference of the hemisphere = 31.4 cm

Let r represent the radius of the hemisphere, we have;

2·π·r = 31.4 cm

r = 31.4/(2 × π) ≈ 4.9975 cm

The volume of the hemisphere = 2/3 × π × r³ = 2/3 × π × (31.4/(2 × π))³ ≈ 261.4 cm³

The volume of the syringe = π × d²/4 × h = π × 2.37²/4 × 6.8 ≈ 29.998 cm³

The number of syringe filled with water that would be needed to fill the semi-sphere = (The volume of the hemisphere)/(The volume of the syringe)

Therefore;

The number of syringe filled with water that would be needed to fill the semi-sphere = 261.4 cm³/(29.998 cm³) ≈ 8.714 syringes.

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3 years ago

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For the function P(x) = x3 − 9x, at the point (2, −10), find the following. (a) the slope of the tangent to the curve (b) the in

Shalnov [3]

Answer:

3, in both a), b)

Step-by-step explanation:

a) The slope of the line tangent to the curve that passes through the point (2,-10) is equal to the derivative of p at x=2.

Using differentiation rules (power rule and sum rule), the derivative of p(x) for any x is $p'(x)=3x^2-9$ . In particular, the value we are looking for is $p'(2)=3(2^2)-9=12-9=3$ .